| Abstract: | It is proved that, for any metabelian Mal'tsev algebra M over a field of characteristic  2,3, there is an alternative algebra A such that the algebra M can be embedded in the commutator algebra A(-). Moreover, the enveloping alternative algebra A can be found in the variety of algebras with the identity x,y]z,t] = 0. The proof of this result is based on the construction of additive bases of the free metabelian Mal'tsev algebra and the free alternative algebra with the identity x,y]z,t] = 0. |
